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Properties

Label 1368.3.v
Level $1368$
Weight $3$
Character orbit 1368.v
Rep. character $\chi_{1368}(353,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1368.v (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1368, [\chi])\).

Total New Old
Modular forms 976 240 736
Cusp forms 944 240 704
Eisenstein series 32 0 32

Trace form

\( 240 q + 2 q^{3} - 6 q^{9} + O(q^{10}) \) \( 240 q + 2 q^{3} - 6 q^{9} - 18 q^{11} + 8 q^{15} - 108 q^{17} - 6 q^{19} - 72 q^{23} - 1200 q^{25} - 40 q^{27} - 24 q^{31} + 90 q^{33} - 52 q^{39} + 108 q^{43} + 160 q^{45} - 840 q^{49} + 28 q^{51} + 14 q^{57} + 140 q^{63} + 432 q^{65} + 42 q^{67} + 16 q^{69} - 18 q^{73} - 214 q^{75} - 288 q^{77} - 218 q^{81} - 124 q^{87} - 216 q^{89} - 96 q^{91} - 144 q^{93} - 648 q^{95} + 90 q^{97} - 232 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 2}\)